{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Preference Estimation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook produces the following Tables and Figures found in the Online Appendix of the paper. \n",
    "\n",
    "* Table A.1: MPL_risk.tex\n",
    "* Table A.2: risk_frequencies.tex\n",
    "* Table A.3: risk_estimates.tex\n",
    "* Table A.4: time_frequencies.tex\n",
    "* Table A.5: time_estimates.tex\n",
    "* Figure A.1: risk_bounds.png\n",
    "* Figure A.2: risk_density.png\n",
    "* Figure OA.3: risk_time.png "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading the data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We load the dataset. You will need to adjust path to where the data is sitting. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_stata('final_data.dta',convert_categoricals=False)\n",
    "df['qc'] = np.where(df['province']==6,1,0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now map the lottery answers into a variable that records the last switch from A to B. We keep the inconsistent switch patterns and count the last switch. We drop those with no switch at 10 because they do not have a stricly increasing utility function. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1     174\n",
       "2      28\n",
       "3      37\n",
       "4     118\n",
       "5     497\n",
       "6     488\n",
       "7     437\n",
       "8     295\n",
       "9     244\n",
       "10    295\n",
       "11    392\n",
       "Name: lottery, dtype: int64"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['lottery'] = np.where(df['lottery_1']=='B',1,0)\n",
    "for i in range(2,11):\n",
    "    df['lottery'] = np.where((df['lottery_'+str(i)]=='B') & (df['lottery_'+str(i-1)]=='A'),i,df['lottery'])\n",
    "df['lottery'] = np.where(df['lottery']==0,11,df['lottery']) \n",
    "df['lottery'].value_counts().sort_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3005"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['lottery'].value_counts().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = df[df['lottery']<11]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We get the following distribution of choices (Table A.2 in Online Appendix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>total</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>frequency</th>\n",
       "      <td>174.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>37.0</td>\n",
       "      <td>118.0</td>\n",
       "      <td>497.0</td>\n",
       "      <td>488.0</td>\n",
       "      <td>437.0</td>\n",
       "      <td>295.0</td>\n",
       "      <td>244.0</td>\n",
       "      <td>295.0</td>\n",
       "      <td>2613.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>percent</th>\n",
       "      <td>6.7</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.4</td>\n",
       "      <td>4.5</td>\n",
       "      <td>19.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>16.7</td>\n",
       "      <td>11.3</td>\n",
       "      <td>9.3</td>\n",
       "      <td>11.3</td>\n",
       "      <td>100.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               1     2     3      4      5      6      7      8      9     10  \\\n",
       "frequency  174.0  28.0  37.0  118.0  497.0  488.0  437.0  295.0  244.0  295.0   \n",
       "percent      6.7   1.1   1.4    4.5   19.0   18.7   16.7   11.3    9.3   11.3   \n",
       "\n",
       "            total  \n",
       "frequency  2613.0  \n",
       "percent     100.0  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table = pd.DataFrame(data=[df['lottery'].value_counts().sort_index(),100*df['lottery'].value_counts().sort_index()/len(df)],\n",
    "                     index=['frequency','percent'])\n",
    "table['total'] = table.sum(axis=1)\n",
    "table = table.round(1)\n",
    "with open('risk_frequencies.tex','w') as tf:\n",
    "    tf.write(table.to_latex())\n",
    "table    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's check if we skip sequences with refersals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1829\n",
       "1     784\n",
       "Name: flag_reversals, dtype: int64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['flag_reversals'] = 0\n",
    "for i in range(2,11):\n",
    "    cond = (df['lottery_'+str(i)]=='A') & (df['lottery_'+str(i-1)]=='B') & (df['flag_reversals']==0) \n",
    "    df['flag_reversals'] = np.where(cond,1,df['flag_reversals'])\n",
    "df['flag_reversals'].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run this line if you want to drop those sequences. The number of observations is produced below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#df = df[df['flag_reversals']==0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2613"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Risk Aversion: The payoff table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lotteries have the following properties:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[20, 16] [39, 1] [0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. ]\n"
     ]
    }
   ],
   "source": [
    "payA, payB = [20,16], [39,1]\n",
    "pr = np.arange(0.1,1.1,0.1)\n",
    "print(payA,payB,pr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Expected payoffs are"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.100000 16.400000 4.800000\n",
      "0.200000 16.800000 8.600000\n",
      "0.300000 17.200000 12.400000\n",
      "0.400000 17.600000 16.200000\n",
      "0.500000 18.000000 20.000000\n",
      "0.600000 18.400000 23.800000\n",
      "0.700000 18.800000 27.600000\n",
      "0.800000 19.200000 31.400000\n",
      "0.900000 19.600000 35.200000\n",
      "1.000000 20.000000 39.000000\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[None, None, None, None, None, None, None, None, None, None]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[print('{0:2f} {1:3f} {2:3f}' .format(p,p*payA[0]+(1-p)*payA[1],p*payB[0]+(1-p)*payB[1])) for p in pr]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's setup a crra utility function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def crra(wealth,sigma):\n",
    "    if sigma==1.0:\n",
    "        return np.log(wealth)\n",
    "    else :\n",
    "        return wealth**(1-sigma)/(1.0-sigma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And expected utility $EU(w,p,\\Delta,\\sigma)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def eu(wealth,p,pay,sigma):\n",
    "    return p*crra(wealth+pay[0],sigma) + (1-p)*crra(wealth+pay[1],sigma)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a given choice $j$ where switch, we have a lower bound defined by the equality expected utility of the two lotteries:\n",
    "\\begin{eqnarray}\n",
    "EU(w,p_j,\\Delta_{A,j},\\sigma_{\\min}) = EU(w,p_j,\\Delta_{B,j},\\sigma_{\\min}) \n",
    "\\end{eqnarray}\n",
    "and similarly for the higher bound:\n",
    "\\begin{eqnarray}\n",
    "EU(w,p_{j-1},\\Delta_{A,j-1},\\sigma_{\\max}) = EU(w,p_{j-1},\\Delta_{B,j-1},\\sigma_{\\max}) \n",
    "\\end{eqnarray}\n",
    "\n",
    "We can construct a function that solves for $\\sigma$: $(\\sigma_{i,\\min},\\sigma_{i,\\max})$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import brentq\n",
    "\n",
    "def q(sigma,wealth,p,payA,payB):\n",
    "    return eu(wealth,p,payA,sigma) - eu(wealth,p,payB,sigma)\n",
    "\n",
    "def solve(wealth,p,payA,payB):\n",
    "    sigma = brentq(q,-2.0,2.0,args=(wealth,p,payA,payB))\n",
    "    return sigma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "cuts = [solve(0.0,p,payA,payB) for p in pr[:-1]]\n",
    "cuts.insert(0,-np.inf)\n",
    "cuts.append(np.inf)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next table produces the cutoffs found in Table A.1 of the Online Appendix. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>lottery</th>\n",
       "      <th>sigma_min</th>\n",
       "      <th>sigma_max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>-inf</td>\n",
       "      <td>-1.671737</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>-1.671737</td>\n",
       "      <td>-0.916175</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>-0.916175</td>\n",
       "      <td>-0.461898</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>-0.461898</td>\n",
       "      <td>-0.122135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>-0.122135</td>\n",
       "      <td>0.163649</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>0.163649</td>\n",
       "      <td>0.426106</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>7</td>\n",
       "      <td>0.426106</td>\n",
       "      <td>0.688535</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>8</td>\n",
       "      <td>0.688535</td>\n",
       "      <td>0.980796</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>9</td>\n",
       "      <td>0.980796</td>\n",
       "      <td>1.376354</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10</td>\n",
       "      <td>1.376354</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   lottery  sigma_min  sigma_max\n",
       "0        1       -inf  -1.671737\n",
       "1        2  -1.671737  -0.916175\n",
       "2        3  -0.916175  -0.461898\n",
       "3        4  -0.461898  -0.122135\n",
       "4        5  -0.122135   0.163649\n",
       "5        6   0.163649   0.426106\n",
       "6        7   0.426106   0.688535\n",
       "7        8   0.688535   0.980796\n",
       "8        9   0.980796   1.376354\n",
       "9       10   1.376354        inf"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "js = range(1,11)\n",
    "bounds = pd.DataFrame(data=None,index=None,columns=['lottery','sigma_min','sigma_max'])\n",
    "bounds['lottery'] = js\n",
    "bounds['sigma_min'] = cuts[:-1]\n",
    "bounds['sigma_max'] = cuts[1:]\n",
    "bounds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = df.merge(bounds,on='lottery')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following cell produces Figure A.1 found in the paper. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
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     },
     "metadata": {
      "needs_background": "light"
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     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from statsmodels.distributions.empirical_distribution import ECDF\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "\n",
    "smin = df['sigma_min'].tolist()\n",
    "ecdf_min = ECDF(smin)\n",
    "smin.sort()\n",
    "\n",
    "smax = df['sigma_max'].tolist()\n",
    "ecdf_max = ECDF(smax)\n",
    "smax.sort()\n",
    "\n",
    "\n",
    "plt.figure()\n",
    "plt.step(ecdf_min(smin),smin,label='$\\sigma_{\\min}$')\n",
    "plt.step(ecdf_max(smax),smax,label='$\\sigma_{\\max}$')\n",
    "plt.ylabel('risk aversion ($\\sigma$)')\n",
    "plt.xlabel('cumulative distribution function')\n",
    "plt.legend(loc=2)\n",
    "plt.savefig('risk_bounds.png',dpi=1200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    2613.000000\n",
       "mean            -inf\n",
       "std              NaN\n",
       "min             -inf\n",
       "25%        -0.122135\n",
       "50%         0.163649\n",
       "75%         0.688535\n",
       "max         1.376354\n",
       "Name: sigma_min, dtype: float64"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['sigma_min'].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Do a Table for the paper with the MPL and data on bounds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "MPL = pd.DataFrame(data=None,columns=['p(A)','w(A,0)','1-p(A)','w(A,1)','p(B)','w(B,0)','1-p(B)','w(B,1)'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "MPL['p(A)'] = [0.1+0.1*s for s in range(0,10)]\n",
    "MPL['1-p(A)'] = 1 - MPL['p(A)']\n",
    "MPL['w(A,0)'] = 20.0\n",
    "MPL['w(A,1)'] = 16.0\n",
    "MPL['p(B)']   = MPL['p(A)']\n",
    "MPL['1-p(B)']   = 1.0-MPL['p(B)']\n",
    "MPL['w(B,0)'] = 39.0\n",
    "MPL['w(B,1)'] = 1.0\n",
    "MPL['Ew(A)'] = MPL['p(A)']*MPL['w(A,0)']+MPL['1-p(A)']*MPL['w(A,1)'] \n",
    "MPL['Ew(B)'] = MPL['p(B)']*MPL['w(B,0)']+MPL['1-p(B)']*MPL['w(B,1)'] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gap(gamma,prob,wa,wb):\n",
    "    eua = prob*crra(wa[0],gamma) + (1-prob)*crra(wa[1],gamma)\n",
    "    eub = prob*crra(wb[0],gamma) + (1-prob)*crra(wb[1],gamma)\n",
    "    return eua - eub"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "nchoice = np.max(MPL.index.values)\n",
    "for i in range(0,nchoice):\n",
    "    p = MPL.loc[i,'p(A)']\n",
    "    wa = [MPL.loc[i,'w(A,0)'],MPL.loc[i,'w(A,1)']]\n",
    "    wb = [MPL.loc[i,'w(B,0)'],MPL.loc[i,'w(B,1)']]\n",
    "    MPL.loc[i,'upper'] = np.round(brentq(gap,-5.0,5.0,args=(p,wa,wb)),3)\n",
    "for i in range(1,nchoice+1):\n",
    "    MPL.loc[i,'lower'] = MPL.loc[i-1,'upper']\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "MPL = MPL[['p(A)','w(A,0)','1-p(A)','w(A,1)','Ew(A)','p(B)','w(B,0)','1-p(B)','w(B,1)','Ew(B)','lower','upper']]\n",
    "MPL.columns = ['$p_A$','$w_{A,1}$','1-$p_A$','$w_{A,2}$','$Ew_A$','$p_B$','$w_{B,1}$','1-$p_B$','$w_{B,2}$','$Ew_B$','$\\\\sigma_{\\\\min}$','$\\\\sigma_{\\\\max}$']\n",
    "MPL.index = [x for x in range(1,11)]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is Table A.1 in paper."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
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       "      <td>16.0</td>\n",
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       "      <td>0.3</td>\n",
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       "      <td>12.4</td>\n",
       "      <td>-0.916</td>\n",
       "      <td>-0.462</td>\n",
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       "      <td>0.4</td>\n",
       "      <td>39.0</td>\n",
       "      <td>0.6</td>\n",
       "      <td>1.0</td>\n",
       "      <td>16.2</td>\n",
       "      <td>-0.462</td>\n",
       "      <td>-0.122</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.5</td>\n",
       "      <td>20.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>16.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>39.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>1.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>-0.122</td>\n",
       "      <td>0.164</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.6</td>\n",
       "      <td>20.0</td>\n",
       "      <td>0.4</td>\n",
       "      <td>16.0</td>\n",
       "      <td>18.4</td>\n",
       "      <td>0.6</td>\n",
       "      <td>39.0</td>\n",
       "      <td>0.4</td>\n",
       "      <td>1.0</td>\n",
       "      <td>23.8</td>\n",
       "      <td>0.164</td>\n",
       "      <td>0.426</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.7</td>\n",
       "      <td>20.0</td>\n",
       "      <td>0.3</td>\n",
       "      <td>16.0</td>\n",
       "      <td>18.8</td>\n",
       "      <td>0.7</td>\n",
       "      <td>39.0</td>\n",
       "      <td>0.3</td>\n",
       "      <td>1.0</td>\n",
       "      <td>27.6</td>\n",
       "      <td>0.426</td>\n",
       "      <td>0.689</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.8</td>\n",
       "      <td>20.0</td>\n",
       "      <td>0.2</td>\n",
       "      <td>16.0</td>\n",
       "      <td>19.2</td>\n",
       "      <td>0.8</td>\n",
       "      <td>39.0</td>\n",
       "      <td>0.2</td>\n",
       "      <td>1.0</td>\n",
       "      <td>31.4</td>\n",
       "      <td>0.689</td>\n",
       "      <td>0.981</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.9</td>\n",
       "      <td>20.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>16.0</td>\n",
       "      <td>19.6</td>\n",
       "      <td>0.9</td>\n",
       "      <td>39.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>1.0</td>\n",
       "      <td>35.2</td>\n",
       "      <td>0.981</td>\n",
       "      <td>1.376</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>39.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>39.0</td>\n",
       "      <td>1.376</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    $p_A$  $w_{A,1}$  1-$p_A$  $w_{A,2}$  $Ew_A$  $p_B$  $w_{B,1}$  1-$p_B$  \\\n",
       "1     0.1       20.0      0.9       16.0    16.4    0.1       39.0      0.9   \n",
       "2     0.2       20.0      0.8       16.0    16.8    0.2       39.0      0.8   \n",
       "3     0.3       20.0      0.7       16.0    17.2    0.3       39.0      0.7   \n",
       "4     0.4       20.0      0.6       16.0    17.6    0.4       39.0      0.6   \n",
       "5     0.5       20.0      0.5       16.0    18.0    0.5       39.0      0.5   \n",
       "6     0.6       20.0      0.4       16.0    18.4    0.6       39.0      0.4   \n",
       "7     0.7       20.0      0.3       16.0    18.8    0.7       39.0      0.3   \n",
       "8     0.8       20.0      0.2       16.0    19.2    0.8       39.0      0.2   \n",
       "9     0.9       20.0      0.1       16.0    19.6    0.9       39.0      0.1   \n",
       "10    1.0       20.0      0.0       16.0    20.0    1.0       39.0      0.0   \n",
       "\n",
       "    $w_{B,2}$  $Ew_B$  $\\sigma_{\\min}$  $\\sigma_{\\max}$  \n",
       "1         1.0     4.8              NaN           -1.672  \n",
       "2         1.0     8.6           -1.672           -0.916  \n",
       "3         1.0    12.4           -0.916           -0.462  \n",
       "4         1.0    16.2           -0.462           -0.122  \n",
       "5         1.0    20.0           -0.122            0.164  \n",
       "6         1.0    23.8            0.164            0.426  \n",
       "7         1.0    27.6            0.426            0.689  \n",
       "8         1.0    31.4            0.689            0.981  \n",
       "9         1.0    35.2            0.981            1.376  \n",
       "10        1.0    39.0            1.376              NaN  "
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MPL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('MPL_risk.tex','w') as tf:\n",
    "    tf.write(MPL.to_latex(escape=False))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Risk Aversion: Bounded Response Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will write a model for risk aversion that allows to impute within bounds. The model is not exactly same as in Andersen et al but makes sense I think. Let's assume $\\sigma$ follows a $N(\\mu,\\eta^2)$. The mean $\\mu$ is a function of $x_i$, a vector of observed characteristics, $\\mu=x_i\\beta$. Then the probability of observing choice $y_i=j$ is given by:\n",
    "\n",
    "\\begin{eqnarray}\n",
    "\\Pr(y_i=j) = \\Phi(\\frac{\\sigma_{j,\\max} - x_i\\beta}{\\eta}) - \\Phi(\\frac{\\sigma_{j,\\min} - x_i\\beta}{\\eta}) \n",
    "\\end{eqnarray}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will add characteristics in the mean $\\mu$ another day. We can define a likelihood that can be maximized to estimate these values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import norm\n",
    "Phi = norm(0,1).cdf\n",
    "def loglike(par,x,sigma_max,sigma_min):\n",
    "    m = x.shape[1]\n",
    "    beta = par[:m]\n",
    "    eta = np.exp(par[m])\n",
    "    xb = np.matmul(x,beta)\n",
    "    bmax = (sigma_max - xb)/eta\n",
    "    bmin = (sigma_min - xb)/eta\n",
    "    p = Phi(bmax) - Phi(bmin)\n",
    "    p = np.where(p<1e-10,1e-10,p)\n",
    "    lli = np.log(p)\n",
    "    return -np.sum(lli)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3    1629\n",
       "2     616\n",
       "1     253\n",
       "0     115\n",
       "Name: fin3, dtype: int64"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['fin3'] = 0\n",
    "correct = [1,3,2]\n",
    "domains = ['interest','inflation','asset']\n",
    "for i,s in enumerate(domains):\n",
    "    df['fin3'] += np.where(df['finlit_'+s]==str(correct[i]),1,0)\n",
    "df['fin3'].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['fin3'] = np.where(df['fin3']==3,1,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import minimize\n",
    "\n",
    "df['const'] = 1.0\n",
    "df['agep'] = (df['age']-df['age'].mean())/df['age'].std()\n",
    "\n",
    "xnames = ['agep','male','married','educ4_3','educ4_4','qc','fin3','const']\n",
    "x = df[xnames].to_numpy()\n",
    "k = x.shape[1]\n",
    "ipar = [0.0 for i in range(k)]\n",
    "ipar.append(np.log(0.25))\n",
    "ipar = np.array(ipar)\n",
    "opt = minimize(loglike,ipar,args=(x,df['sigma_max'].values,df['sigma_min'].values),method='BFGS')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1      39\n",
       "2     439\n",
       "3     832\n",
       "4    1303\n",
       "Name: educ4, dtype: int64"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['educ4'].value_counts().sort_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "pnames = ['age (z)','male','married','some college','college','quebec','FL 3 correct','constant']\n",
    "pnames.append('$\\\\eta$')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numdifftools as nd\n",
    "H = nd.Hessian(loglike)(opt.x,x,df['sigma_max'].values,df['sigma_min'].values)\n",
    "invH = np.linalg.inv(H)\n",
    "se = np.sqrt(np.diag(invH))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is Table A.3 in online Appendix. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>point estimate</th>\n",
       "      <th>standard error</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>age (z)</th>\n",
       "      <td>-0.023</td>\n",
       "      <td>0.018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>male</th>\n",
       "      <td>-0.071</td>\n",
       "      <td>0.037</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>married</th>\n",
       "      <td>0.013</td>\n",
       "      <td>0.038</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>some college</th>\n",
       "      <td>-0.059</td>\n",
       "      <td>0.053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>college</th>\n",
       "      <td>-0.092</td>\n",
       "      <td>0.051</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>quebec</th>\n",
       "      <td>0.039</td>\n",
       "      <td>0.036</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FL 3 correct</th>\n",
       "      <td>-0.022</td>\n",
       "      <td>0.039</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>constant</th>\n",
       "      <td>0.483</td>\n",
       "      <td>0.056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\eta$</th>\n",
       "      <td>0.899</td>\n",
       "      <td>0.015</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              point estimate  standard error\n",
       "age (z)               -0.023           0.018\n",
       "male                  -0.071           0.037\n",
       "married                0.013           0.038\n",
       "some college          -0.059           0.053\n",
       "college               -0.092           0.051\n",
       "quebec                 0.039           0.036\n",
       "FL 3 correct          -0.022           0.039\n",
       "constant               0.483           0.056\n",
       "$\\eta$                 0.899           0.015"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta = opt.x[:k]\n",
    "eta = np.exp(opt.x[k])\n",
    "se[k] = eta*se[k]\n",
    "results = pd.DataFrame(data=np.append(beta,eta),index=pnames,columns=['point estimate'])\n",
    "results['standard error'] = se\n",
    "results = results.round(3)\n",
    "with open('risk_estimates.tex','w') as tf:\n",
    "    tf.write(results.to_latex(escape=False))\n",
    "results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now compute the posterior. We have: \n",
    "\n",
    "\\begin{eqnarray}\n",
    "E(\\sigma|y_i=j) &=& \\mu + \\eta\\frac{\\phi(\\frac{\\sigma_{j,\\min}-\\mu}{\\eta}) - \\phi(\\frac{\\sigma_{j,\\max}-\\mu}{\\eta})}{\\Phi(\\frac{\\sigma_{j,\\max}-\\mu}{\\eta}) -\\Phi(\\frac{\\sigma_{j,\\min}-\\mu}{\\eta}) } \n",
    "\\end{eqnarray}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "phi = norm(0,1).pdf\n",
    "mu = np.matmul(x,beta)\n",
    "num = phi((df['sigma_min'].values - mu)/eta) - phi((df['sigma_max'].values - mu)/eta)\n",
    "den = Phi((df['sigma_max'].values - mu)/eta) - Phi((df['sigma_min'].values - mu)/eta)\n",
    "sigma = mu + eta*(num/den)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['sigma'] = sigma"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some stats on $\\sigma$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    2613.000000\n",
       "mean        0.395838\n",
       "std         0.884982\n",
       "min        -1.991030\n",
       "25%         0.023960\n",
       "50%         0.296220\n",
       "75%         0.830908\n",
       "max         1.868477\n",
       "Name: sigma, dtype: float64"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['sigma'].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.13662456946039037"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(df['sigma']<0.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Means conditional on being in a particular bin (response)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "lottery\n",
       "1    -1.978296\n",
       "2    -1.200737\n",
       "3    -0.666485\n",
       "4    -0.283980\n",
       "5     0.023822\n",
       "6     0.295572\n",
       "7     0.556174\n",
       "8     0.830814\n",
       "9     1.166233\n",
       "10    1.835798\n",
       "Name: sigma, dtype: float64"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby(['lottery'])['sigma'].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally an estimate of the density. This is Figure A.2 in Online Appendix. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "metadata": {
      "needs_background": "light"
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     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import gaussian_kde\n",
    "f = gaussian_kde(df['sigma'])\n",
    "plt.figure()\n",
    "s = df['sigma'].tolist()\n",
    "s.sort()\n",
    "plt.plot(s,f(s))\n",
    "plt.xlabel('$\\sigma$')\n",
    "plt.ylabel('density')\n",
    "plt.savefig('risk_density.png',dpi=1200)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Time Preference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['time'] = np.where(df['time_1']=='B',1,0)\n",
    "for i in range(2,11):\n",
    "    df['time'] = np.where((df['time_'+str(i)]=='B') & (df['time_'+str(i-1)]=='A'),i,df['time'])\n",
    "df['time'] = np.where(df['time']==0,11,df['time']) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is Table A.4 in Online Appendix. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
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       "frequency  872.0  265.0  135.0  161.0  252.0  176.0  125.0  101.0  122.0   \n",
       "percent     33.4   10.1    5.2    6.2    9.6    6.7    4.8    3.9    4.7   \n",
       "\n",
       "              10     11   total  \n",
       "frequency  132.0  272.0  2613.0  \n",
       "percent      5.1   10.4   100.0  "
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table = pd.DataFrame(data=[df['time'].value_counts().sort_index(),100*df['time'].value_counts().sort_index()/len(df)],\n",
    "                     index=['frequency','percent'])\n",
    "table['total'] = table.sum(axis=1)\n",
    "table = table.round(1)\n",
    "with open('time_frequencies.tex','w') as tf:\n",
    "    tf.write(table.to_latex())\n",
    "table "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1     872\n",
       "2     265\n",
       "3     135\n",
       "4     161\n",
       "5     252\n",
       "6     176\n",
       "7     125\n",
       "8     101\n",
       "9     122\n",
       "10    132\n",
       "11    272\n",
       "Name: time, dtype: int64"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['time'].value_counts().sort_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>pattern_time</th>\n",
       "      <th>flag_reversals</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>BBBBBBBBBB</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>AAAAAAAAAA</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>BBBBBBBBBB</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>BBBBBBBBBB</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>BBBBBBBBBB</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  pattern_time  flag_reversals\n",
       "0   BBBBBBBBBB               0\n",
       "1   AAAAAAAAAA               0\n",
       "2   BBBBBBBBBB               0\n",
       "3   BBBBBBBBBB               0\n",
       "4   BBBBBBBBBB               0"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['flag_reversals'] = 0\n",
    "for i in range(2,11):\n",
    "    cond = (df['time_'+str(i)]=='A') & (df['time_'+str(i-1)]=='B') & (df['flag_reversals']==0) \n",
    "    df['flag_reversals'] = np.where(cond,1,df['flag_reversals'])\n",
    "df[['pattern_time','flag_reversals']].head()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    2154\n",
       "1     459\n",
       "Name: flag_reversals, dtype: int64"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['flag_reversals'].value_counts()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Time Preference: The payoff table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(12.0, 12.6), (12.0, 13.2), (12.0, 13.8), (12.0, 14.4), (12.0, 15.0), (12.0, 15.6), (12.0, 16.2), (12.0, 16.8), (12.0, 17.4), (12.0, 18.0)]\n"
     ]
    }
   ],
   "source": [
    "payA, payB = [12.0 for i in range(10)], np.linspace(12.60,18.0,10)\n",
    "print([(payA[i],payB[i]) for i in range(10)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "def edu(cons,delay,sigma,delta):\n",
    "    return (delta**delay)*crra(cons,sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "def solve(sigma,consA,consB):\n",
    "    delta = crra(consA,sigma)/crra(consB,sigma)\n",
    "    return delta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Find bounds on time preference for each respondent\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['sigma'] = np.where(df['sigma']==np.nan,df['sigma'].mean(),df['sigma'])\n",
    "df['delta_min'] = 0.0\n",
    "df['delta_max'] = 0.0\n",
    "for i in range(len(df)):\n",
    "    sig = df.loc[i,'sigma']\n",
    "    c = df.loc[i,'time']-1\n",
    "    if (c==0):\n",
    "        df.loc[i,'delta_min'] = solve(sig,payA[c],payB[c])\n",
    "        df.loc[i,'delta_max'] = np.Inf       \n",
    "    elif (c==10):\n",
    "        df.loc[i,'delta_min'] = -np.Inf\n",
    "        df.loc[i,'delta_max'] = solve(sig,payA[c-1],payB[c-1])\n",
    "    else :\n",
    "        df.loc[i,'delta_min'] = solve(sig,payA[c],payB[c])\n",
    "        df.loc[i,'delta_max'] = solve(sig,payA[c-1],payB[c-1])\n",
    "        \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "time         5.443159\n",
       "delta_min    0.931175\n",
       "delta_max    0.945419\n",
       "sigma        0.518468\n",
       "dtype: float64"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.loc[(df.delta_max!=np.Inf) & (df.delta_min!=-np.Inf),['time','delta_min','delta_max','sigma']].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Time Preference: Bounded Response Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "ipar = [0.01 for i in range(k)]\n",
    "xnames = ['agep','male','married','educ4_3','educ4_4','qc','fin3','const']\n",
    "x = df[xnames].to_numpy()\n",
    "ipar.append(np.log(0.25))\n",
    "ipar = np.array(ipar)\n",
    "opt = minimize(loglike,ipar,args=(x,df['delta_max'].values,df['delta_min'].values),method='BFGS')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00491649, 0.01005381, 0.01019123, 0.01488993, 0.01417805,\n",
       "       0.00991822, 0.01083749, 0.0156988 , 0.02319151])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H = nd.Hessian(loglike)(opt.x,x,df['delta_max'].values,df['delta_min'].values)\n",
    "invH = np.linalg.inv(H)\n",
    "se = np.sqrt(np.diag(invH))\n",
    "se"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "beta = opt.x[:k]\n",
    "eta = np.exp(opt.x[k])\n",
    "se[k] = eta*se[k]\n",
    "results = pd.DataFrame(data=np.append(beta,eta),index=pnames,columns=['point estimate'])\n",
    "results['se'] = se\n",
    "with open('time_estimates.tex','w') as tf:\n",
    "    tf.write(results.round(3).to_latex(escape=False))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is Table A.5 in Online Appendix. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>point estimate</th>\n",
       "      <th>se</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>age (z)</th>\n",
       "      <td>0.009588</td>\n",
       "      <td>0.004916</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>male</th>\n",
       "      <td>-0.034375</td>\n",
       "      <td>0.010054</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>married</th>\n",
       "      <td>-0.001363</td>\n",
       "      <td>0.010191</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>some college</th>\n",
       "      <td>-0.004238</td>\n",
       "      <td>0.014890</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>college</th>\n",
       "      <td>-0.004246</td>\n",
       "      <td>0.014178</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>quebec</th>\n",
       "      <td>0.005390</td>\n",
       "      <td>0.009918</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FL 3 correct</th>\n",
       "      <td>0.049873</td>\n",
       "      <td>0.010837</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>constant</th>\n",
       "      <td>0.925341</td>\n",
       "      <td>0.015699</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\eta$</th>\n",
       "      <td>0.210955</td>\n",
       "      <td>0.004892</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              point estimate        se\n",
       "age (z)             0.009588  0.004916\n",
       "male               -0.034375  0.010054\n",
       "married            -0.001363  0.010191\n",
       "some college       -0.004238  0.014890\n",
       "college            -0.004246  0.014178\n",
       "quebec              0.005390  0.009918\n",
       "FL 3 correct        0.049873  0.010837\n",
       "constant            0.925341  0.015699\n",
       "$\\eta$              0.210955  0.004892"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "phi = norm(0,1).pdf\n",
    "mu = np.matmul(x,beta)\n",
    "num = phi((df['delta_min'].values - mu)/eta) - phi((df['delta_max'].values - mu)/eta)\n",
    "den = Phi((df['delta_max'].values - mu)/eta) - Phi((df['delta_min'].values - mu)/eta)\n",
    "delta = mu + eta*(num/den)\n",
    "df['delta'] = delta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    2613.000000\n",
       "mean        0.969928\n",
       "std         0.202798\n",
       "min         0.234221\n",
       "25%         0.855082\n",
       "50%         0.968589\n",
       "75%         1.125430\n",
       "max         1.396313\n",
       "Name: delta, dtype: float64"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['delta'].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is Figure OA.3 in Online Appendix. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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   ],
   "source": [
    "# library & dataset\n",
    "import seaborn as sns\n",
    "\n",
    "\n",
    "# Basic 2D density plot\n",
    "sns.set_style(\"white\")\n",
    "ax = sns.kdeplot(df.sigma, df.delta)\n",
    "ax.set(xlabel='$\\sigma$ (risk aversion)', ylabel='$\\\\beta$ (discount factor)')\n",
    "ax.get_figure().savefig('risk_time.png',dpi=1200)\n",
    "#sns.plt.show()\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>delta</th>\n",
       "      <th>sigma</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>delta</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.513882</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
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      "text/plain": [
       "          delta     sigma\n",
       "delta  1.000000  0.513882\n",
       "sigma  0.513882  1.000000"
      ]
     },
     "execution_count": 58,
     "metadata": {},
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   ],
   "source": [
    "df[['delta','sigma']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once preferences have been created, they are save to a dataset which is then merged back with the main dataset. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "output = df[['id','sigma','delta']]\n",
    "output.to_stata('preferences.dta',write_index=False)"
   ]
  },
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   "execution_count": null,
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